Theorems · Inductive type · category theory
SemiSimplexCategory
Type
The category whose objects are denoted ⦋n⦌ₛ for n : ℕ and
morphisms ⦋n⦌ₛ ⟶ ⦋m⦌ₛ are order embeddings Fin (n.len + 1) ↪o Fin (m.len + 1).
(This identifies to a wide subcategory of the category SemiSimplex, which
has the "same" objects, and morphisms Fin (n.len + 1) →o Fin (m.len + 1),
see the faithful functor SemiSimplexCategory.toSimplexCategory.)
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 0 from the axioms · uses no axioms
Around this declaration
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Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by27
Results whose statement or proof uses this declaration.
- SemiSimplexCategory.lenstatement and proof · cited by 6
- SemiSimplexCategory.homEquivstatement and proof · cited by 4
- SemiSimplexCategory.toSimplexCategorystatement and proof · cited by 4
- SemiSimplexCategory.homOfMonostatement and proof · cited by 3
- SSet.N.toSemiSimplexCategorystatement · cited by 3
- SemiSimplexCategory.extstatement and proof · cited by 1
- SemiSimplexCategory.hom_extstatement and proof · cited by 1
- SemiSimplexCategory.mk.injstatement · cited by 1
- SemiSimplexCategory.mk.noConfusionstatement · cited by 1
- SemiSimplexCategory.Homstatement and proof · cited by 0
- SemiSimplexCategory.casesOnstatement and proof · cited by 0
- SemiSimplexCategory.ctorIdxstatement and proof · cited by 0